Surrounding rock and lining are composite structures with asymmetric mechanical properties. Understanding the mechanical properties and failure characteristics of rock–concrete composites is crucial for gaining insights into the mechanisms that induce disasters in deep-underground environments. Uniaxial compression and acoustic emission tests were conducted on rock–concrete composite specimens cured at temperatures of 20 °C, 40 °C, 60 °C, and 80 °C, with interface angles of 15°, 30°, 45°, 60°, 75°, and 90° respectively. The results indicated that the specimens’ strength decreased at increasing geothermal temperatures. The composites with an 80 °C curing temperature and a 60° interface angle exhibited the lowest strength. A higher geothermal temperature significantly reduced the number of cracks in the concrete component during composite failure and mitigated the influence of the inclined interface angle. The failure modes of the specimens include axial penetration splitting, interface shear, Y-shaped fracture, and interface splitting–concrete shear failure. Finally, a model relating the strength of the rock–concrete composite to the inclined interface angle and the geothermal temperature was derived and verified against the experimental results with a relative error of 9.8%. The findings have significant implications for the safety and stability of tunnels in high-temperature conditions.